中文摘要：

该文证明了若交换Hopf代数在余代数C上的扭余作用的coassociator是卷积可逆的，那么该扭余作用也是可逆的．在这种情形下，给出了余代数C的正则上同调的定义，并且证得每个可逆的扭余作用可以提升到H的系数属于C的一个三次正则上同调类，且扭余作用的obstruction是平凡的当且仅当该扭余作用对应着一个cleft余扩张．

英文摘要：

In this paper, we show that the twisted coactions of commutative Hopf algebras H on coalgebras C are invertible if the corresponding coassociators are convolution invertible. In this case, we define the regular cohomology and show that every invertible twisted coaction gives rise to a regular cohomology class of H with coefficients in C of degree three. We also show that the obstruction for ρ vanishes if and only if the the twisted coaction ρ is corresponding to a cleft coextension.